Operator equation

S is the set of all R -> R functions.
T is a S -> S function such that:

T(f o g) = (T(f) o g) * T(g) for every f and g in S,
where (f o g)(x) = f(g(x)) and (f * g)(x) = f(x) * g(x).

Are there non-constant solutions?

Thank you,
Theron